diff --git a/Lib/pickletools.py b/Lib/pickletools.py
index 6614df7..cfd5fcc 100644
--- a/Lib/pickletools.py
+++ b/Lib/pickletools.py
@@ -2128,11 +2128,11 @@
 
 Exercise the INST/OBJ/BUILD family.
 
->>> import random
->>> dis(pickle.dumps(random.getrandbits, 0))
-    0: c    GLOBAL     'random getrandbits'
-   20: p    PUT        0
-   23: .    STOP
+>>> import pickletools
+>>> dis(pickle.dumps(pickletools.dis, 0))
+    0: c    GLOBAL     'pickletools dis'
+   17: p    PUT        0
+   20: .    STOP
 highest protocol among opcodes = 0
 
 >>> from pickletools import _Example
diff --git a/Lib/test/pickletester.py b/Lib/test/pickletester.py
index 3ed84fb..51dd0fc 100644
--- a/Lib/test/pickletester.py
+++ b/Lib/test/pickletester.py
@@ -545,6 +545,16 @@
             got = self.loads(p)
             self.assertEqual(n, got)
 
+    def test_float(self):
+        test_values = [0.0, 4.94e-324, 1e-310, 7e-308, 6.626e-34, 0.1, 0.5,
+                       3.14, 263.44582062374053, 6.022e23, 1e30]
+        test_values = test_values + [-x for x in test_values]
+        for proto in protocols:
+            for value in test_values:
+                pickle = self.dumps(value, proto)
+                got = self.loads(pickle)
+                self.assertEqual(value, got)
+
     @run_with_locale('LC_ALL', 'de_DE', 'fr_FR')
     def test_float_format(self):
         # make sure that floats are formatted locale independent with proto 0
diff --git a/Misc/NEWS b/Misc/NEWS
index 53cd724..5f8eda5 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -139,6 +139,9 @@
 Library
 -------
 
+- Issue #1672332: fix unpickling of subnormal floats, which was
+  producing a ValueError on some platforms.
+
 - Issue #3881: Help Tcl to load even when started through the
   unreadable local symlink to "Program Files" on Vista.
 
diff --git a/Modules/_pickle.c b/Modules/_pickle.c
index 6536e6f..5813fd4 100644
--- a/Modules/_pickle.c
+++ b/Modules/_pickle.c
@@ -2958,7 +2958,8 @@
     errno = 0;
     d = PyOS_ascii_strtod(s, &endptr);
 
-    if (errno || (endptr[0] != '\n') || (endptr[1] != '\0')) {
+    if ((errno == ERANGE && !(fabs(d) <= 1.0)) ||
+        (endptr[0] != '\n') || (endptr[1] != '\0')) {
         PyErr_SetString(PyExc_ValueError, "could not convert string to float");
         return -1;
     }